Sunday and Monday are named after the sun and moon (English < Germanic), and Tuesday through Friday are named after Anglo-Saxon/Germanic gods. This seems consistent enough so far, but then we come to the oddbal;: Saturday.

Ignoring the mandatory -day, this is the only Latin-derived name of the lot. Why are six of the week-day names Germanic and one Romanic?

3 Answers
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The names of the week were originally Roman according to the Oxford English Dictionary:

The Latin days of the week in imperial Rome were named after the planets, which in turn were named after gods (see discussion at week n.). In most cases the Germanic names have substituted for the Roman god's name that of a comparable one from the Germanic pantheon, but in the case of Saturday, the Roman name was retained and borrowed.

For example, Tuesday was originally named after Mars, but then switched to Tiw:

Originally cognate with or formed similarly to Old Frisian tīesdei , Old High German ziestag , Middle High German zīstag (German regional (south-eastern) Ziestag , (south-eastern and Swiss) Ziestig ) < the genitive of the Germanic base of the name of (the god) Tiw (see note) + the Germanic base of day n., after post-classical Latin dies Martis day of (the planet) Mars (4th cent. but probably earlier; frequently from c1135 in British sources; compare classical Latin Martis diēs

When the days were renamed, Mars was equivalent to Tiig (Tiw):

eOE Corpus Gloss. 76/2 Mars, martis, tiig.

The OED also notes that the Germanic people would have originally used the Roman names, but then subsequently changed them (by Old English, Mars didn't factor into Tuesday at all):

The English names, Sunday, Monday, etc., belong to an astrological week which, quite independently of the Jewish–Christian week, arose from the practice of assigning the successive hours to the seven planets in the order of their distance, and then naming each whole day (of 24 hours) from the planet supposed to rule its first hour. The planetary names, Dies Solis, Dies Lunæ, Dies Martis, etc., came into common use in the Roman empire, and were adopted in translated form by the English (before they came to Britain) and other Germanic peoples; the names Mars, Mercurius, etc., being apprehended as names of Roman gods, were rendered by the names of the Teutonic deities supposed to correspond to these

There is no further note on why Saturday was allowed to remain a reference to Saturn, however.

Most likely, "Saturn" was retained as a solution for the problems that arose when Germans tried to translate the seven day week.

First, the tradition of a seven-day workweek, with all weekdays being named after planets, was adopted by Northern Europe from the Mediterranean Latin and Greek cultures; that's a pretty straightforward matchup: Thor was Saturn, Tyr/Tiu was Mars, Odin was Jupiter, Freyja was the personification of Venus, Sunna was the personification of the Sun, and Mani was the personification of the Moon.

This is all largely the same as in the Latinized week, and you can see it pretty easily in French (or any other Romance language): "Lundi" is "Luna's Day", "Mardi" is "Mars' day", "Mercredi" is "Mercury's day", "Jeudi" is "JUpiter's day", and "Vendredi" is "Venus' day"; today, the remaining words are "Samedi" (a corruption of "Sabbath", "Sabato" in Italian) and "Dimanche" ("Domenica" in It., or "Holy Day"), but these are Christian imports. The words for these days were originally, in Latin, just as they are in English, today: "Sunday" was "Dies Solis", or "Day of the Sun", and "Saturday" was "Dies Saturni", or "Day of Saturn".

What should be obvious from the above is that the Norse didn't just transliterate the days of the week in perfect order, but adapted them according both to the characteristics of their gods as well as to the order in which the planets were named in the Latin/Greek tradition. Largely, the order was preserved, but one important substitution was made: Mercury, being the planet of the god Loki, the great traitor and progenitor of all evil, dropped out. Thus, Jupiter shifted forward to take its place as "Wodin's Day", as did Saturn/Thor for the fourth day, making "Thor's Day".

So -- how did the one Latinized form, Saturn, creep its way into English? Because there were only five planets back then, and Mercury/Loki, the traitor, wasn't something the Norse much wanted to use in their day-to-day time-telling. So that left four planets (Venus, Mars, Jupiter, Saturn), + Sun & Moon. One day was left over. Some word was needed to fill it.

Presumably, Mercury was out regardless of what name it used (i.e. -- the Norse didn't want to use the word in any language, even a foreign one), so which other planet should double up? "Saturn" was a word that represented time itself (going back to the Greco-Roman tradition of Kronos/Saturn), and was a deity whose characteristics and qualities didn't correspond to any other in the Norse pantheon. Further, it doubled up on Thor, who was a beloved deity to the Norse and the great hero-leader/tragic figure of the entire pantheon. Finally, since "Thor" and "Saturn" sounded completely different, there was no reason to even bother with inventing a new word: "Saturn's Day" could just remain in place, without bothering to change a thing. Thus, Saturday stuck.

Long story short: we can't really be sure of the exact mechanisms, but this is probably something close to how it happened.

Do you have sources for this interpretation of the Jupiter/Wodin Loki/Mercury connection, or are you… ahem, forgive me … winging it? Gaius Cornelius Tacitus in his work Germania identifies the chief deity of the germanic peoples with Mercury, so there seems to be no basis for your proposed substitution…
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ghoppeSep 14 '11 at 16:03

@ghoppe - I'd like to see some sources too, but Tacitus' writings on the society of Germanic tribes I wouldn't consider the most reliable either. He was, after all, a Roman with his own worldview to try to wedge the Germans into. irminsul.org/arc/004bl.html argues persuasively that prehistory Germanic tribes may have only really used larger phenomena, like constellations, the Milky Way, the Auroa Borealis, etc. in their mythology. An ancient Roman (who likes to think everyone's gods are the same, just with different names) would have a lot of trouble with that concept.
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T.E.D.Sep 14 '11 at 19:54

@T.E.D. an excellent point. It is likely that Tacitus saw whatever peculiar ritual the German tribes did to venerate their god, and then thought "we do the same thing when we venerate Mercury! They must be worshipping Mercury!"
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ghoppeSep 14 '11 at 22:12

@ghoppe - Right. Or its possible he equated Mercury with one of the Norse gods that a nearby tribe happened to favor due to similar mythological attributes (having nothing to do with oddly-moving stars at all).
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T.E.D.Sep 14 '11 at 22:43

The association of the Norse gods with these planets has long been established by historical anthropology. Virtually the entire world over, gods which are associated as "tricksters" -- like Hermes/Mercury, in Rome, or even in the Americas, like with Humwawa -- have been associated with Mercury. You can look in the classic "Hamlets Mill", by Giorgio de Santillana and Hertha von Dechend on this association (it has to do with the difficulty and unpredictability of Mercury's path). Archaeoastronomy is a legitimate academic discipline, but relatively new.
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Kyle PearsonSep 15 '11 at 4:06

Interpretatio germanica is the practice by the Germanic peoples of identifying the Roman gods with the names of Germanic deities. This started to occur around the 1st century CE when both cultures came into closer contact. This is thought to be the mechanism by which the Roman names for the days of the week.

So the problem with this interpretation of the translated days of the week, according to Rudolf Simek, is that while the correspondence between Jupiter and Thor is fairly obvious, (what with the thunder and the lightning and whatnot) for the other figures we must rely on speculation as too little is known about the role the gods played in the then-contemporary beliefs of the Germanic people.

However, Tacitus said that the Rhineland tribes chiefly worshipped Mercury. Jonas of Babbio writing in The Life of Columbanus around 642 CE identified Mercury with Woden. It's unclear whether the Anglo-Saxons regarded Woden as their "chief" deity at the time, or if they picked that up from the invading Danes who held Óðinn as the king of the gods.

So although we don't necessarily know precisely why some particular Germanic gods were identified with other Roman deities, it is fairly evident they were and the days of the week were translated. But the question remains, why did Saturday stick around? Why wasn't a substitution made for that day? Many other languages made substitutions for the Hebrew sabbath, but not Old English.

There's an old Anglo-Saxon poem Solomon and Saturn which is basically a "riddle contest" between the wisest king of the land of Israel and the Roman god, done in the style of Norse poetic eddas. I haven't been able to pin down when it was written, I think in the 9th or 10th centuries. So I take this as some evidence that Saturn wasn't lost to Anglo-Saxon folklore. In the poem, he represented the pagan and eastern tradition, held in contrast to the Christian tradition and faith represented by Solomon. So perhaps this is a case where the name of saturday didn't really change because Saturn wasn't an obscure foreign god, but rather a well-known (although still foreign) entity from folklore.

I don't think anyone knows for sure why Saturday "stuck" while the other days were transformed in Old English. We can only speculate.

EDIT

OK, I've unearthed another interesting tidbit. In Anglo-saxon, Saturday is Sæterdæg or Sæterndæg. The word sætere means "setter", "seducer" or "insidiator". Coincidence? I've seen various sources that say Sætere was worshipped as a "shadowy" Anglo-Saxon deity (not sure about the reliability of these sources), and/or the name was associated with Loki, who was well known as being the trickster.

Of course, this begs the question: was the word sætere coined from Saturn in early germanic history? Was it a coincidence that saturn's day sounded like a nickname for Loki and thus the Latin name for Saturday needed to be only marginally changed to fit the german pantheon? Or did the early anglo-saxons just keep the Roman name for the day virtually unchanged?

And then there's the Norse god Surtr … but let's not muddy the waters any more…